$A$ steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text{steel}} = 1.2 \times 10^{-5} {}^{\circ} C^{-1}\right]$

The density of a substance at $0^{\circ}C$ is $10 \, g/cm^3$ and at $100^{\circ}C$,its density is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is:

Steel rails are laid with gaps to allow for thermal expansion. Each track is $10 \ m$ long,when laid at a temperature of $17^{\circ} C$. The maximum temperature that can be reached is $45^{\circ} C$. The gap to be kept between the two segments of the railway track is $(\alpha_{\text{steel}} = 1.3 \times 10^{-5} /^{\circ} C)$. (in $mm$)

$A$ pendulum clock shows the correct time at $20^{\circ}C$. During summer days,when the temperature rises to $40^{\circ}C$,what will be the time change in the clock in one day (in $.64$)? (Given: $\alpha = 10^{-5} {^{\circ}C}^{-1}$)

$A$ steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \,m$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $= 10 \times 10^{-6} \,K^{-1}$) (in $^{\circ} C$)

$A$ steel tape $1 \; m$ long is correctly calibrated for a temperature of $27.0 \; ^{\circ}C$. The length of a steel rod measured by this tape is found to be $63.0 \; cm$ on a hot day when the temperature is $45.0 \; ^{\circ}C$. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is $27.0 \; ^{\circ}C$? (Coefficient of linear expansion of steel $\alpha = 1.20 \times 10^{-5} \; K^{-1}$)